The present invention relates to a fiber optic gyro of a zero serrodyne modulation system employing a linear phase ramp voltage.
There has been proposed a wide-dynamic-range, low-drift fiber optic gyro of the type having a biasing phase modulator and a ramp phase modulator connected to the one and the other end of an optical fiber coil, respectively. A biasing voltage and a ramp voltage are applied to the biasing phase modulator and the ramp phase modulator, respectively, to thereby provide a phase difference between two rays of light propagating through the optical fiber coil in opposite directions. The phase difference between the two rays of light which propagate through the optical fiber coil and interfere with each other is detected from the output of a photodetector. The detected output is used to control the polarity and the frequency of the ramp voltage so that the phase difference may assume a predetermined value.
FIG. 1 shows an example of such a conventional fiber optic gyro.
Light 12 emitted from a light source 11 is provided via an optical coupler 13 and a polarizer 14 to an optical coupler 15, wherein it is split into two rays of light 5a and 5b. The one light 5a and the other light 5b are supplied to an optical fiber coil 17 at the one and the other end 17a and 17b thereof, respectively, and propagate therethrough as right-handed light and left-handed light. The two rays of light 7a and 7b having thus propagated through the optical fiber coil 17 are supplied therefrom at the ends 17b and 17a to the optical coupler 15, wherein they interfere with each other. The resulting interference light 9 is provided via the polarizer 14 and the optical coupler 13 to a photodetector 19 for conversion into an electric signal as in ordinary fiber optic gyros.
A biasing phase modulator 21 is disposed between the optical coupler 15 and the one end 17a of the optical fiber coil 17 and a ramp phase modulator 22 between the optical coupler 15 and the other end 17b of the optical fiber coil 17. A biasing voltage Bi is applied from an oscillator 31 to the biasing phase modulator 21 for phase shifting the light 5a to be supplied to the optical fiber coil 17 at the one end 17a thereof and the light 7b having propagated through the optical fiber coil 17 from the other end 17b thereof and to be supplied to the optical coupler 15 from the one end 17a of the optical fiber coil 17. At the same time, a ramp voltage Ra is applied from a ramp voltage generator 40 to the ramp phase modulator 22 for phase shifting the light 5b to be supplied from the other end 17b of the optical fiber coil 17 and the light 7a having propagated through the optical fiber coil 17 from the one end 17 a thereof and to be supplied from the other end 17b of the optical fiber coil 17 to the optical coupler 15. The output Va of a photodetector 19 is applied to a phase difference detect/control section 50 described later, wherein the phase difference between the two rays of light 7a and 7b interfering with each other in the optical coupler 15 is detected as described later. The output Ve of the phase difference detect/control section 50 is applied to the ramp voltage generator 40 to control the polarity and the frequency of the ramp voltage Ra so that the above-mentioned phase difference may reach a predetermined value, that is, the sum .DELTA..phi. of a Sagnac phase difference .DELTA..phi..sub.s which is caused by the application of an angular rate .OMEGA. to the optical fiber coil 17 and the phase difference .DELTA..phi..sub.r which is caused by the application of the ramp voltage Ra to the ramp phase modulator 22 may be zero or an integral multiple of 2.pi. rad.
The biasing voltage Bi is a sine-wave voltage of a frequency f.sub.m the half period of which corresponds to the time .tau. necessary for the propagation of the two rays of light 5a and 5b through the optical fiber coil 17 as shown in FIG. 2. The phase modulation by the biasing phase modulator 21 supplied with such a biasing voltage is to provide a phase difference of .pi./2 rad. between the two rays of light 7a and 7b which have propagated through the optical fiber coil 17 in opposite directions and interfere with each other, thereby setting an operating point of the fiber optic gyro.
The ramp voltage Ra goes positive or negative as depicted in FIG. 3. By the phase modulation in the ramp phase modulator 22 supplied with such a ramp voltage the two rays of light 7a and 7b which have propagated through the optical fiber coil 17 in opposite directions and interfere with each other are phase shifted from 0 to 2 k.pi. rad. (where k=.+-.1, .+-.2, . . . ), up to .+-.2.pi. in practice, as indicated by .phi..sub.a and .phi..sub.b in FIG. 4. By controlling the period T of the ramp voltage Ra the changing ratios (i.e. gradients) of the phase shifts .phi..sub.a and .phi..sub.b of the two rays of light 7a and 7b are changed, by which the difference between the phase shifts .phi..sub.a and .phi..sub.b, that is, the phase difference .DELTA..phi..sub.r, is controlled to cancel the Sagnac phase difference .DELTA..phi..sub.s as mentioned above.
The difference between the phase difference between the two rays of light 7a and 7b interfering with each other in the optical coupler 15 and the phase difference between them introduced by the biasing phase modulator 21 is equal to the sum of the Sagnac phase difference .DELTA..phi..sub.s and the phase difference .DELTA..phi..sub.r introduced by the ramp phase modulator 22 as given below: EQU .DELTA..phi.=.DELTA..phi..sub.s +.DELTA..phi..sub.r ( 1)
As is well-known in the art, the Sagnac phase difference .DELTA..phi..sub.s is expressed as follows: ##EQU1## where R is the radius of the optical fiber coil 17, L is the length of the optical fiber coil 17, .lambda. is the wavelength of light which propagates through the optical fiber coil 17, and C is the velocity of light in a vacuum.
As described above, in the ramp phase modulator 22, the light 5b which is supplied to the optical fiber coil 17 at its one end 17b is subjected to the phase shift .phi..sub.b corresponding to the value of the ramp voltage Ra at that time and after the elapse of time .tau. the light 7a which has propagated through the optical fiber coil 17 from the end 17a thereof and is supplied to the optical coupler 15 through the end 17b of the optical fiber coil 17 is subjected to the phase shift .phi..sub.a corresponding to the value of the ramp voltage Ra at that time. When the angular rate .OMEGA. is applied clockwise and the Sagnac phase difference .DELTA..phi..sub.s goes negative, the ramp voltage Ra is controlled to be positive by the output Ve of the phase difference detect/control section 50 as shown at the left-hand side in FIG. 3. In this instance, the phase shifts .phi..sub.a and .phi..sub.b bear such a relationship as shown at the left-hand side in FIG. 4 and the phase difference .DELTA..phi..sub.r resulting from the application of the ramp voltage Ra to the ramp phase modulator 22 goes positive. Where the angular/rate .OMEGA. is applied counterclockwise and the Sagnac phase difference .DELTA..phi..sub.s goes positive, the ramp voltage Ra is made negative by the output Ve of the phase difference detect/control section 50 as shown at the right-hand side in FIG. 3, in consequence of which the phase shifts .phi..sub.a and .phi..sub.b bear such a relationship as depicted at the right-hand side in FIG. 4, rendering the phase difference .DELTA..phi..sub.r negative.
As will be seen from FIG. 4, letting the period and the frequency of the ramp voltage Ra be represented by T and f.sub.R, respectively, the following equation holds: ##EQU2## Letting the refractive index of light in the optical fiber coil 17 be represented by n, the following relationship exists: ##EQU3## Hence, substitution of Eq. (4) into Eq. (3) gives the following equation: ##EQU4## Thus, by controlling the polarity and the frequency f.sub.R of the ramp voltage Ra so that the phase difference .DELTA..phi. expressed by Eq. (1) may be reduced to zero, that is, EQU .DELTA..phi..sub.r =-.DELTA..phi..sub.s ( 6)
the frequency f.sub.R is obtained from Eqs. (2) and (5) as follows: ##EQU5## From Eq. (7) the input angular/rate .OMEGA. is expressed by the following equation: ##EQU6## In the case where the angular rate .OMEGA. is applied clockwise, i.e. in the negative direction and the ramp voltage Ra goes positive, k becomes +1, and in the case where the input angular rate .OMEGA. is applied counterclockwise, i.e. in the positive direction and the ramp voltage Ra goes negative, k becomes -1. Accordingly, the direction and the magnitude of the input angular rate .OMEGA. can be measured from the polarity and the frequency f.sub.R of the ramp voltage Ra. The actual fiber optic gyro includes a polarity detector for detecting the polarity of the ramp voltage Ra and a counting circuit for counting the frequency f.sub.R (or period T) of the ramp voltage Ra, but they are not shown in FIG. 1 for the sake of brevity. Incidentally, in the case where the angular rate .OMEGA. is applied to the optical fiber coil 17, the coil 17 makes one rotation in a time 2.pi./.OMEGA. and the number of ramp pulses which are generated in this period, 2.pi..multidot.f.sub.R /.OMEGA., becomes -4.pi.R/(kn .lambda.) from Eq. (7) and is constant irrespective of the input angular rate .OMEGA.. The number of pulses per rotation is referred to as a scale factor.
Letting the frequency and the angular frequency of the biasing voltage Bi be represented by f.sub.m and .omega..sub.m, respectively, the output Va of the photodetector 19 is expressed as follows: ##EQU7## In the above, Vdc is a DC component, Ka and Kb are constants, J.sub.2n (x) and J.sub.2n+1 (x) are Bessel functions of the first kind, the first term of Eq. (9) is a DC component, the second term is a component of a frequency which is an even-numbered multiple of the frequency f.sub.m of the biasing voltage Bi, and the third term is a component of a frequency which is an odd-numbered multiple of the frequency f.sub.m.
In the phase difference detect/control section 50, only that one of the components expressed in the third term of Eq. (9) which has the frequency f.sub.m when n=0 is extracted from the output Va of the photodetector 19, the component of the frequency f.sub.m is synchronously detected by a reference signal of the same frequency, and the following detected output is obtained as the output having detected the phase difference between the two rays of light 7a and 7b which interfere with each other in the optical coupler 15: EQU Vd=Kc.multidot.J.sub.1 (x)sin .DELTA..phi. (10)
where Kc is a constant.
Since the polarity and the frequency f.sub.R of the ramp voltage Ra is controlled so that the phase difference .DELTA..phi. may be reduced to zero as described previously, however, a component Vm of the frequency f.sub.m contained in the third term of Eq. (9) becomes very low in level as shown in FIG. 5, whereas a component Vs of a frequency 2f.sub.m contained in the second term of Eq. (9) becomes considerably higher in level as shown. In addition, the frequency f.sub.m of the biasing voltage Bi is usually set so that its half period corresponds to the time .tau. necessary for the propagation of light 5a and 5b through the optical fiber coil 17, as follows: EQU f.sub.m =1/2.tau. (11)
Substitution of Eq. (11) into Eq. (4) gives EQU f.sub.m =C/2nL (12)
More specifically, assuming, for example, that the refractive index n of light in the optical fiber coil 17 is 1.47 and the length L of the optical fiber coil 17 is 300 m, the frequency f.sub.m rises as high as about 430 kHz. In the case where the output Va of the photodetector 19 is applied directly to a band-pass filter whose center frequency is f.sub.m, its pass bandwidth becomes so wide that it is impossible to accurately eliminate the component Vs of the frequency 2f.sub.m from the output Va and extract only the component Vm of the frequency f.sub.m at a sufficient level.
To avoid this, the output Va of the photodetector 19 is mixed with a local signal of a frequency f.sub.ca =f.sub.m +f.sub.r or f.sub.cd =f.sub.m -f.sub.r, slightly different from the frequency f.sub.m, by which the component V.sub.m of the frequency f.sub.m is converted to an intermediate frequency f.sub.r sufficiently lower than the frequency f.sub.m. The mixed output is applied to a band-pass filter whose center frequency is the intermediate frequency f.sub.r and only the component of the intermediate frequency f.sub.r is obtained from the band-pass filter. This component is synchronously detected by a reference signal of the same frequency f.sub.r, by which the detected output Vd expressed by Eq. (10) is obtained.
This will be described with reference to FIG. 1. The output Va of the photodetector 19 is applied to a preamplifier 51, by which its DC component Vdc is removed and its AC component is amplified. The AC component is fed to a frequency mixer 52, in which it is mixed with a local signal Sca of the frequency f.sub.ca from an oscillator 32. The frequency f.sub.ca is a little higher than the frequency f.sub.m as shown in FIG. 5. The frequency mixer 52 produces an output Vc containing components Vr and Vh of the difference and the sum of the frequencies f.sub.m and f.sub.ca, a component Vl of the difference between the frequencies 2f.sub.m and f.sub.ca, etc. The output Vc of the frequency mixer 52 is applied to a band-pass filter 53 whose center frequency is the intermediate frequency f.sub.r. The intermediate frequency f.sub.r is selected to be 10 kHz, for instance. Since the center frequency f.sub.r of the band-pass filter 53 is selected to be markedly lower than the frequency f.sub.m, the pass bandwidth of the filter 53 can be made sufficiently narrow. Of the components contained in the output Vc of the frequency mixer 52, the components except for the component Vr of the frequency f.sub.r are of the frequencies higher than the frequency f.sub.cb (=f.sub.m -f.sub.r); so that the filter 53 provides only the component Vr of the frequency f.sub.r, that is, the component of the frequency f.sub.r converted from the component Vm of the frequency f.sub.m contained in the output Va of the photodetector 19.
The component Vr of the intermediate frequency f.sub.r thus provided from the band-pass filter 53 is amplified by an AC amplifier 54 to a sufficient level and is then supplied to a synchronous detector 55, in which it is synchronously detected by a reference signal Sr of the frequency f.sub.r and from which the detected output Vd expressed by Eq. (10) is obtained as the detected output of the phase difference between the light 7a and 7b interfering with each other in the optical coupler 15. The output Vd of the synchronous detector 55 is fed to a PID (Proportional plus Integral plus Derivative) filter 56, the output Ve of which is provided, as the output of the phase difference detect/control section 50, to the ramp voltage generator 40 to control the polarity and the frequency f.sub.R of the ramp voltage Ra so that the phase difference .DELTA..phi. may be reduced to zero.
In the frequency mixer 52 a local signal Scb of the frequency f.sub.cb =f.sub.m -f.sub.r may be used in place of the local signal Sca of the frequency f.sub.ca =f.sub.m +f.sub.r.
The reference signal Sr of the frequency f.sub.r for synchronous detection is produced as follows: The biasing voltage Bi of the frequency f.sub.m, yielded from the oscillator 31, and the local signal Sca or Scb of the frequency f.sub.ca =f.sub.m +f.sub.r or f.sub.cb =f.sub.m -f.sub.r, provided from the oscillator 32, are mixed together in a frequency mixer 33. The mixed output is supplied to a band-pass filter 34, from which only a signal of the intermediate frequency f.sub.r is obtained, and this signal is provided to a waveform shaping circuit 35, from which the reference signal Sr is obtained as a rectangular-wave signal of the frequency f.sub.r.
The ramp voltage Ra which is applied to the ramp phase modulator 22 is shown to be an ideal ramp voltage which has no fly-back time in FIG. 3, but in practice, it is impossible to reduce the fly-back time of the ramp voltage Ra to zero and the ramp voltage Ra has a fly-back time of tens of nanoseconds or more. Furthermore, it is also impossible, in practice, owing to the characteristics of the ramp voltage generator 40 and the ramp phase modulator 22 that the maximum values of the phase shifts .phi..sub.a and .phi..sub.b by the ramp phase modulator 22 are set accurately to .+-.2.pi. rad.
Since the fly-back time exists in the ramp voltage Ra and since the maximum values of the phase shift .phi..sub.a and .phi..sub.b do not become .+-.2.pi. rad accurately, the phase difference between the two rays of light 7a and 7b which have propagated through the optical fiber coil 17 in the opposite directions and interfere with each other has an error composed of the fundamental wave component of the frequency f.sub.R of the ramp voltage and harmonic components of frequencies which are integral multiples of the fundamental frequency. This error appears as upper and lower side-band components U1, U2, . . . and L1, L2, . . . of the component Vm of the frequency f.sub.m in the output Va of the photodetector 19, as shown in FIG. 7. In addition, since the frequency f.sub.R of the ramp voltage Ra varies with the input angular velocity .OMEGA., the frequencies of the upper and lower side-band wave components U1, U2, . . . and L1, L2, . . . also vary with the input angular velocity .OMEGA..
On this account, when the frequency f.sub.R is equal to a twofold value of the frequency f.sub.r of the reference signal Sr for the aforementioned synchronization in the phase difference detect/control section 50, the upper or lower side-band wave component U1 or L1 agrees with a frequency f.sub.ia =f.sub.m +2f.sub.r or f.sub.ib =f.sub.m- 2f.sub.r, respectively, as shown in FIG. 8 and when a threefold value of the frequency f.sub.R is equal to the twofold value of the frequency f.sub.r, the upper or lower side band wave component U3 or L3 agrees with the frequency f.sub.ia or f.sub.ib, respectively, as depicted in FIG. 9. In the presence of a specific input angular velocity which provides f.sub.R =f.sub.r /n (where n is 1, 2, 3, . . . ), any one of the upper side band wave components U1, U2, . . . or any one of the lower side band wave components L1, L2, . . . agrees with the image frequency f.sub.ia or f.sub.ib of the frequency f.sub.m corresponding to the frequency f.sub.ca or f.sub.cb of the local signal Sca or Scb. Hence, the upper or lower side-band wave is mixed with the local signal Sca or Scb in the frequency mixer 52, that is, the above-mentioned side-band wave is converted to the intermediate frequency f.sub.r together with the component Vm of the frequency f.sub.m. The side-band component thus converted to the intermediate frequency f.sub.r is provided via the band-pass filter 53 to the AC amplifier 54 and the amplified output is supplied to the synchronous detector 55, thus introducing a scale factor error into the output of the fiber optic gyro.
The scale factor error becomes maximum when the upper or lower side-band wave component U1 or L1 corresponding to the fundamental wave component of the frequency f.sub.R of the ramp voltage Ra agrees with the image frequency f.sub.ia or f.sub.ib, respectively, as shown in FIG. 8. On the other hand, when the upper or lower side-band wave component U3 or L3 corresponding to a harmonic component which is an integral multiple of the frequency f.sub.R agrees with the image frequency f.sub.ia or f.sub.ib, the scale factor error decreases in general as shown in FIG. 9.
The ramp phase modulator 22 usually has a single-mode optical waveguide formed as by diffusing titanium into an electro-optic crystal as of lithium niobate and a pair of electrodes disposed opposite across the optical waveguide. By the application of the ramp voltage Ra across the pair of electrodes the refractive index of the optical waveguide is changed to shift the phase of light passing therethrough. In this instance, a portion of the light passing through the optical waveguide leaks out therefrom in accordance with the value of the applied voltage, and consequently, the intensity of light passing through the optical waveguide is modulated by the ramp voltage Ra and variation in the light intensity appears, in the output Va of the photodetector 19, as a fundamental wave component R.sub.1 of the frequency f.sub.R of the ramp voltage Ra and harmonic wave components R.sub.2, . . . , R.sub.n, . . . of frequencies which are integral multiples of the frequency f.sub.R, as depicted in FIG. 10.
When the above-mentioned fundamental wave component R.sub.1 or harmonic wave components R.sub.2, . . . , R.sub.n, . . . agree with the image frequency f.sub.ia or f.sub.ib in the presence of a particular input angular rate, the fundamental wave component R.sub.1 or harmonic wave components R.sub.2, . . . , R.sub.n, . . . are mixed with the local signal Sca or Scb in the frequency mixer 52 of the phase difference detect/control section 50, by which the above-said component or components are converted to the intermediate frequency f.sub.r together with the component Vm of the frequency f.sub.m. The fundamental wave component or harmonic wave components thus converted to the intermediate frequency f.sub.r are provided via the band-pass filter 53 to the AC amplifier 54 and the amplified output is fed to the synchronous detector 55, thus producing a scale factor error in the output of the fiber optic gyro.
FIG. 11 shows the above-mentioned scale factor variations with the input angular rate .OMEGA. in the conventional fiber optic gyro shown in FIG. 1, the frequency f.sub.r being 10 kHz. The number of output pulses of the fiber optic gyro corresponding to the frequency f.sub.R of the ramp voltage Ra varies with the input angular rate .OMEGA., but the scale factor of the output from the fiber optic gyro, that is, the number of output pulses of the fiber optic gyro per rotation should be constant regardless of the input angular rate .OMEGA. as mentioned previously. However, as mentioned above, the maximun values of the phase shifts .phi..sub.a and .phi..sub.b do not accurately become 2.pi. rad. because of the presence of the fly-back time in the ramp voltage Ra or the characteristics of the ramp voltage generator 40 and the ramp phase modulator 22, or since the intensity of light passing through the optical waveguide is modulated by the ramp voltage Ra in the ramp phase modulator 22; so that the number of output pulses of the fiber optic gyro per rotation deviates from a predetermined value in the vicinity of a particular input angular rate as depicted in FIG. 11, inducing a scale factor error in the output of the fiber optic gyro. The reason for a particularly large scale factor error in the vicinity of an input angular rate of 34.degree./sec in FIG. 11 is that the upper or lower side-band wave component U1 or L1 corresponding to the fundamental wave component of the frequency f.sub.R of the ramp voltage Ra agrees with the image frequency f.sub.ia or f.sub.ib as referred to previously with respect to FIG. 8.